How can I use Q-criterion to visualize vortex?
 

I am simulating incompressible boundary layer transition flow. I separate the flow velocity (u, v, w) into a base flow part (U, V, W) and a disturbance part (u’ ,v’ ,w’,). I use the below equations to calculate Q (second invariant of velocity gradient tensor):
Ω= (0.5*{dudy}-0.5*{dvdx})**2+(0.5*{dudz}-0.5*{dwdx})**2+
(0.5*{dvdx}-0.5*{dudy})**2+(0.5*{dvdz}-0.5*{dwdy})**2+
(0.5*{dwdx}-0.5*{dudz})**2+(0.5*{dwdy}-0.5*{dvdz})**2

S={dudx}**2+(0.5*{dvdx}+0.5*{dudy})**2+(0.5*{dwdx} +0.5*{dudz})**2+
(0.5*{dvdx}+0.5*{dudy})**2+{dvdy}**2+(0.5*{dwdy}+0 .5*{dvdz})**2 +
(0.5*{dwdx}+0.5*{dudz})**2+(0.5*{dwdy}+0.5*{dvdz}) **2+{dwdz}**2

Q=0.5*(Ω-S)

My questions are:
(1) In the calculation of velocity gradient tensor, should I use the total flow or disturbance flow quantities?

(2) I have tried both in (1), but the values of dudx is around 1.0e2 pre second in the transition region and the final Q is around 1.0e5 or larger. Are these values normal? In the papers I read, Q are usually closed to zero about 1.0e-2.

(3) I am using very coarse grid in my simulation (820*80*16 for streamwise, wall-normal and spanwise direction) and I cannot see vortical structures, for example, a ring at the tip and two long legs at the tail as the papers. Is that because of my resolution?
Thank you in advance.

Hi,

I can't understand your notation very well, sorry, but i usually write Q=0.5*(Ω^2-S^2) where Ω is the vorticity magnitude and S the mean strain rate (absolute quantities)
I use the normalized Q-criterion, so the range is -1<Q<1

Hope be helpful

Thanks a lot. After normalization the result looks better.

Hi Atze,

I have also calculated Q-criterion and I wonder how to normalize Q. Is that Q/max(Q)?